THE U1 GAUGE FIELD IN A SUN GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

GU CHAO-HAO

Chinese Physics C> 1978, Vol. 2> Issue(4) : 295-304

THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

GU CHAO-HAO

Futan Unvivercity

Abstract
HTML
Reference
Related

PDF

Abstract：
Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x）（λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_v_λ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.

References

[1]

G. 't Hooft, Nucl. Phys., B79(1974), 276.[2] 侯伯宇、段一士、葛墨林，兰州大学学报(自然科学版)，1975, 2, 26.[3] J. Arafune, P. G. O. Freund and C. J. Goebel, Jour. Math. Phys., 16(1975), 433.[4] T. T. Wu, C. N. Yang, Phys. Rev., D12(1975), 3845;C. N. Yang, "Gauge Fields", (Proc. 1975 Hawaii Conf.).[5] 谷超豪、杨振宁，中国科学，1976, 6, 610; Scientia Sinica, 20 (1977), 177.[6] Z. F. Ezawa and H. C. Tze, Nucl. Phys., B100(1975), 1.[7] W. J. Marciano and H. Pagels, Phys. Rev., D12(1975), 1093.[8] 谷超豪，复旦学报(自然科学版)，1975, 4, 82;中国科学，1976, 3, 320.[9] И. М. Mxanoc, H 3. R., "TIpeArrabneHxA rpyrm BpaiuexHH“rppm}TIopeHUa, , (1958, Mocx日a), 33-34.[10] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press (1962), 354.

[1]	HUANG Wen-Xue , WANG Yue , ZHU Zhi-Chao , TIAN Yu-Lin , XU Hu-Shan , SUN Zhi-Yu , XIAO Guo-Qing , ZHAN Wen-Long . Experimental Study of the High-Voltage Breakdown and Simulations for the RFQ Cooler and Buncher RFQ1L. Chinese Physics C, 2006, 30(S2): 261-264.
[2]	LIU Chang-Long , LU Yi-Ying , YIN LI . Effects of Additional Vacancy-Like Defects Produced by Ion Impealations on Boron Thermal Diffusion in Silicon. Chinese Physics C, 2005, 29(11): 1107-1111.
[3]	HU Xi-Duo , SHAO Ming-Zhu , LUO Shi-Yu , LIU Yong-Sheng , ZHU De-Hai . Average Field Idea and Single Particle Model for 2 Dimension Crystallization Beams(Ⅱ). Chinese Physics C, 2004, 28(2): 196-199.
[4]	Medina Ablikim , HUANG Wei-Cheng , . New Realization of N=2 Supersymmetric QuantumMechanics and Shape Invariance. Chinese Physics C, 2002, 26(4): 338-345.
[5]	Guo Hua . In-medium QMC Model Parameters and Quark Condensation in Nuclear Matter. Chinese Physics C, 1999, 23(5): 459-468.
[6]	Chen Zhongqiu , Shao Changgui , Ma Weichuan . Calculation of Wilson Loop Functionals for Classical and Quantum Gravities. Chinese Physics C, 1998, 22(3): 217-224.
[7]	Yu Hong , Shen Qixing , Zhang Lin . Angular Distribution of Process e⁺e^－→τ⁺τ^－,τ^－→a₁υτ,a₁→ρπ and Characteristics of a₁ Meson. Chinese Physics C, 1994, 18(7): 583-590.
[8]	BES Collaboration . Experimental Study of Resonance f₂(1270) in the J/ψ Hadronic Decay. Chinese Physics C, 1993, 17(2): 97-106.
[9]	Sa Ben-hao , Zhang Xi-zhen , Li Zhu-xia , Shi Yi-jin . A PRIMARY RESEARCH OF THE PHONON RENORMALIZATION OF NUCLEAR FIELD THEORY. Chinese Physics C, 1980, 4(3): 398-400.

Access

Get Citation

GU CHAO-HAO. THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES[J]. Chinese Physics C, 1978, 2(4): 295-304.

GU CHAO-HAO. THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES[J]. Chinese Physics C, 1978, 2(4): 295-304. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1976-09-07
Revised: 1900-01-01

Article Metric

Article Views(2167)
PDF Downloads(247)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

THE U₁ GAUGE FIELD IN A SU_N GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

GU CHAO-HAO

Futan Unvivercity

Received Date: 1976-09-07
Accepted Date: 1900-01-01
Available Online: 1978-08-05

Abstract: Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x）（λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_v_λ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.